An attention-based explanation for some exhaustivity operators

A well-known challenge for accounts of exhaustivity implications is the granularity problem: that adding a non-weakest disjunct to an utterance (e.g., “or both”) may prevent exhaustivity implications. Recent approaches to this problem apply exhaustivity operators either globally, i.e., to the disjunction as a whole, or locally, i.e., to each disjunct separately. This paper seeks to contribute to a better understanding of the operators employed in the globalist strand, which, contrary to globalists’ aims, have not thus far been given any sort of pragmatic motivation. To that end this paper demonstrates that these operators can be derived, wholly or in part, from a pragmatic theory: Attentional Pragmatics (Westera, 2017). The theory centers on the assumption that speakers should not only assert all relevant propositions they hold true, but also draw attention to all relevant propositions they consider possible. This assumption, suitably formalized, overcomes the granularity problem. The current paper formally derives an exhaustivity operator from Attentional Pragmatics and proves that it is in important respects conservative with regard to existing operators.